Mathematics Home / Research Seminars: Graduate Student Colloquium

Time & Location: All talks are on Tuesdays in Gibson 414 at 4:00 PM unless otherwise noted.

Organizer: Nathaniel Vaduthala

**January 15**

**Title**: *TBA*

**Speaker | Tulane University**

**Abstract**: TBA

**Time**: 5:00pm

**Location: **Stanley Thomas 316

**January 24**

**Title**: *Graduate Algebra III: Linguistics*

**Melanie Tian | Tulane University**

**Abstract**:

We introduce the field of mathematical linguistics in two flavors. First we introduce mathematical methods in linguistics, where we give examples on verifying equivalences and non-equivalences using tools such as lambda calculus and determiners as relations. Then we look at two problems on deciphering unfamiliar writing systems: numeral system in Nahuatl, and Transcendental Algebra constructed by Jakob Linzbach.

**Time**: 4:00pm

**Location: **Stanley Thomas 316

**January 31**

**Title**: *Introduction to Spatial Point processes*

**Lan Trinh | Tulane University**

**Abstract**:

Spatial Point processes have been applied in such diverse disciplines as forestry, plant ecology, epidemiology, geography, seismology, materials science, astronomy, telecommunications,… In this talk, I will give an overview about some typical spatial point processes (Poisson, Cox, and Markov point processes) and explain their first- and second-order moments, the useful summary descriptions to explore the spatial point processes at the first glance.

**Time**: 4:00pm

**Location: **Stanley Thomas 316

**February 7**

**Title**: *Introduction to computability theory*

**Haoxi Hu | Tulane University**

**Abstract**:

We have seen a lot of concepts from computability theory, like "computable", Turing Machine, NP and P etc. However, most people don't really have a chance to take a close look at some compatibility theory, so for this talk, I will introduce some basic definitions, theorems, and history from compatibility theory.

**Time**: 4:00pm

**Location: **Gibson 414

**February 14**

**Title**: *Stable Marriage Problem*

**Naufil Sakran | Tulane University**

**Abstract**:

On the wonderful occasion of Valentine's Day, I would like to discuss the stable marriage problem which relates to finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. We then discuss its application in modern technology in the hope that the talk adds flavor to your wonderful day.

**Time**: 4:00pm

**Location: **Gibson 414

**February 28**

**Title**:The Resistive Force Theory and the Reactive Force Theory (Two RFTs)

**Sang-Eun Lee | Tulane University**

**Abstract**:

In this talk, we discuss some immersed structures in the various fluid controlling the scale of Reynolds number from 0 to infinity. The immersed structure in the low Reynolds number flow is developed by the resistive force theory (RFT1), and the analogy on the high Reynolds number flow is called by the reactive force theory (RFT2). We mainly focus on the difficulties of each theory to develop them in computational and mathematical perspectives. For instance, the slender body theory is modified the non-local discrepancy of RFT1. If time permits, the slender body theory on the high Reynolds number flow can be discussed.

**Time**: 4:00pm

**Location: **Gibson 414

**March 7**

**Title**:Transfer Systems

**Peter Marcus | Tulane University**

**Abstract**:

Transfer systems are combinatorial objects that arise in equivariant homotopy theory. They are defined as a certain type of partial order on the set of subgroups of a fixed finite group. The central question is enumerating all possible transfer systems for a given group. I will discuss this and other related results.

**Time**: 4:00pm

**Location: **Gibson 414

**March 21**

**Title**:TBA

**Joshua Agbomola| Tulane University**

**Abstract**:

Ebola virus (EVD) is contingent to African countries and the drastic spread of EVD is devastating over the last decade. The dynamic transmission could be better understood when we consider the various possible transmission routes. Since Ebola virus can only be transmitted via direct pathway; we therefore consider the transmission from human to human, human to fruit bats, fruit bats to fruit bats, human to contaminated environmental surfaces (e.g bedlinen, clothing, doorknobs, needles, or any other medical instrument or other surfaces) and vice versa. A mathematical model was proposed to capture these transmission routes and we check for the necessary conditions to make sure the model is mathematically and biologically meaningful. At the end, the results of the model shown on the graph reveal that the burden of Ebola virus is non-decreased when we incorporate all the transmission pathways. So, considering multiple transmission routes helps in the disease surveillance.

**Time**: 4:00pm

**Location: **Gibson 414

**March 28**

**Title**:Deleterious CAFI promote more large and more small corals in reefs

**Louis Nass | Tulane University**

**Abstract**:

We implement a deterministic size-structured population PDE model to simulate the size-density of a coral reef in a space limited environment. We show that this model has a solution that exists, is unique, and conditionally converges to its steady state solution in time. We introduce coral associated fish and invertebrate (CAFI) interactions and implement CAFI dependence on growth and life expectancy of corals. We compare and contrast different levels of CAFI influence and immigration to understand summary features of our coral reefs. We sample from our size-density to visualize sample environments, and utilize our sampling techniques to show that we can estimate the largest maximum sized coral in a given environment. Finally, we show that deleterious CAFI promote more small and more large corals than beneficial CAFI, and try to understand this from a biological standpoint.

**Time**: 4:00pm

**Location: **Gibson 414

**April 18**

**Title**:A Brief Introduction into Spectral Clustering

**Oliver Orejola | Tulane University**

**Abstract**:

Spectral clustering is a popular unsupervised learning technique in modern data science. In this talk, I will introduce spectral clustering techniques as well as the relevant spectral graph theory in order to understand the heart of these methods. I will also discuss some applications and results relevant to my own research.

**Time**: 4:00pm

**Location: **Gibson 414

**April 25**

**Title**: Generalized Interpolation Problems and Chudnovsky's Conjecture

**Dipendranath Mahato | Tulane University**

**Abstract**:

The problem of interpolation is well known. But what happens when we move to a higher dimension space over any arbitrary Field! While investigating such problem, Gregory Volfovich Chudnovsky gave a conjectural lower bound for the minimal degree of a homogeneous polynomial in the Polynomial ring that vanishes on a given finite set of points with a given set of multiplicities. Later Waldschmidth Constant came into the picture, but how this famous geometrical problem boils down to the Containment Problem of Symbolic Powers and Ordinary Powers is the primary objective of my talk. I will also talk on some recent developments in this area.

**Time**: 4:00pm

**Location: **Gibson 414

**May 2**

**Title**: Scheduling Next Semester's Graduate Colloquiums and Elections

**N/A | Tulane University**

**Abstract**:

We will finalize the speakers for next semester's Graduate Colloquiums and will run elections for AWM, AMS, and SIAM officer positions.

**Time**: 4:00pm

**Location: **Gibson 414

**May 3**

Last Day Of Class